(1) Design of IIR digital filters by means of an interpolation techniqueWe have presented a useful method of designing oneー and twoーdimensional (1-D and 2-D) IIR digital filters, which is guaranteed in principle to be stable, by using the interpolation of the characteristic function of the filter for a set of prescribed values of the function. As an application of the method, we proposed a design method of 1-D IIR digital filters having maximal flatness in the passband and a prescribed steepness in the transition band, the effectiveness of which was confirmed from numerical examples.(2) Research concerning the modeling of stochastic processes based on AR and ARMA modelsConcerning stationary stochastic processes, the YuleーWalker (Y-W) equation is of importance in the representation of the autoーregressive (AR) process. As for solving the Y-W equation, the Levinson algorithm is wellーknown to be standard. Based on both theoretical and experimental investigations, we have first shown that t
… Morehe convergence property of the Levinson algorithm is closely related to the location of zeros of the power spectral function, and derived an efficient algorithm for finding and removing the aboveーmentioned zeros by means of the circuit theoretical approach. Furthermore, on the basis of the theory of canonical representation of Gaussian processes, we discussed the problem of approximating a nonstationary Gaussian process by the ARMA model of a finite order. As a result, a solution to this problem is obtained, which is considered to be useful in designing adaptive IIR digital filters.(3) Research concerning the modeling of 2-D image signals.We have shown that operatorーalgebraic approach is effective in the treatment of 2-D signals in the space domain. We first presented a representation of an operator corresponding to the impulse response of a 2-D linear system, and then clarified basic properties of the composition and decomposition of the operators. We have applied several results mentioned above to the problem of modeling a 2-D signal. As a result. We obtained matrix representation of networks for approximating a given 2-D signal, based on which we presented an algorithm for the modeling of a 2-D signal in the picture or image processing. Less